04747nam 22006975 450 99646636780331620200704065306.03-540-30137-210.1007/b104035(CKB)1000000000212648(SSID)ssj0000204702(PQKBManifestationID)11172535(PQKBTitleCode)TC0000204702(PQKBWorkID)10188717(PQKB)10671856(DE-He213)978-3-540-30137-0(MiAaPQ)EBC3068434(PPN)13412359X(EXLCZ)99100000000021264820101024d2005 u| 0engurnn|008mamaatxtccrModular Algorithms in Symbolic Summation and Symbolic Integration[electronic resource] /by Jürgen Gerhard1st ed. 2005.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2005.1 online resource (XVI, 228 p.) Lecture Notes in Computer Science,0302-9743 ;3218Bibliographic Level Mode of Issuance: Monograph3-540-24061-6 Includes bibliographical references (p. [207]-216) and index.1. Introduction -- 2. Overview -- 3. Technical Prerequisites -- 4. Change of Basis -- 5. Modular Squarefree and Greatest Factorial Factorization -- 6. Modular Hermite Integration -- 7. Computing All Integral Roots of the Resultant -- 8. Modular Algorithms for the Gosper-Petkovšek Form -- 9. Polynomial Solutions of Linear First Order Equations -- 10. Modular Gosper and Almkvist & Zeilberger Algorithms.This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.Lecture Notes in Computer Science,0302-9743 ;3218AlgorithmsNumerical analysisComputer science—MathematicsComputer mathematicsAlgorithm Analysis and Problem Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/I16021Numeric Computinghttps://scigraph.springernature.com/ontologies/product-market-codes/I1701XSymbolic and Algebraic Manipulationhttps://scigraph.springernature.com/ontologies/product-market-codes/I17052Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Computational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Algorithms.Numerical analysis.Computer science—Mathematics.Computer mathematics.Algorithm Analysis and Problem Complexity.Numeric Computing.Symbolic and Algebraic Manipulation.Algorithms.Computational Science and Engineering.005.154.10bclGerhard Jürgenauthttp://id.loc.gov/vocabulary/relators/aut441584BOOK996466367803316Modular Algorithms in Symbolic Summation and Symbolic Integration772838UNISA